EXTENDED X-RAY-ABSORPTION FINE-STRUCTURE (EXAFS) ANALYSIS OF DISORDER AND MULTIPLE-SCATTERING IN COMPLEX CRYSTALLINE SOLIDS

Quantitative determination of local atomic structure in complex materials using extended X-ray absorption fine structure (EXAFS) analysis was tested on eight inorganic compounds of known structure, including natural and synthetic crystalline solids, at ambient conditions. Our aim was to test the accuracy of experimental and theoretical EXAFS standard functions in determining the number of backscattering atoms (N) at a distance (R) beyond the ligating shell of the central absorber atom where effects from disorder, multiple-scattering, and overlapping shells of atoms may significantly influence the EXAFS spectra. These compounds have complicated structures compared to metals and contain Fe, Co, or Ni as the central absorbing atom and mixtures of second-row (C, O, F), third-row (Si, Cl), and fourth-row (Ca, Fe, Co, Ni) atoms as backscatterers. Comparison of results using both experimental phase-shift and amplitude functions (derived from the EXAFS spectra of the compounds) and those calculated from ab initio theory (using the computer code FEFF 5) shows that interatomic distances for single-scattering paths among metal atoms can be determined to within 0.02 Angstrom of values determined independently by X-ray diffraction up to a distance of 4 Angstrom from the central absorber by either method. Theoretical standards calculated using FEFF 5, however, eliminate several drawbacks associated with using experimental standards, such as isolating individual shells of backscattering atoms, obtaining appropriate compounds of high purity and crystallinity, and errors introduced in background subtraction of experimental spectra. Because of the high degree of correlation between N and the Debye-Waller factor (sigma(2)) in the EXAFS function; the ability to determine N for backscatterers of different Z beyond the first shell is limited by incomplete knowledge of sigma(2) for individual absorber-backscatterer paths. For a particular set of backscatterers, N can be determined to better than +/-1 if values for sigma(2) (+/-20-30%) can be estimated. For atoms with a small amount of static disorder, estimation methods include using sigma(2) values from reference compounds, averaging atomic root-mean-square displacements from X-ray diffraction, or using a correlated Debye model. Static disorder, however, can eliminate completely backscattering amplitudes at ambient temperatures for some absorber-backscatterer pairs and is not necessarily predictable in unknown systems. Multiple-scattering (MS) (for k = 3-12 Angstrom(-1)) was found to contribute significant amplitude to EXAFS only if focusing occurred among metal atoms. Nonfocused MS, especially for paths involving oxygen atoms, contributed insignificant amplitude to the EXAFS of these compounds for the k-range analyzed.